Maximal evenness: Difference between revisions

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(a) and (b) above imply that the ME scale will be a [[MOSScales|moment of symmetry scale]].

The probably most popular heptatonic ME scale is the major scale of [[12edo|12edo]]: 2 2 1 2 2 2 1, but also every [http://en.wikipedia.org/wiki/Diatonic_scale diatonic scale] of 12edo is maximally even. Some more detailed examples follow.

The probably most popular heptatonic ME scale is the major scale of [[12edo|12edo]]: 2 2 1 2 2 2 1, but also every [http://en.wikipedia.org/wiki/Diatonic_scale diatonic scale] of 12edo is maximally even. Some more detailed examples follow.

~~For instance, here are all the ME scales available in [[31edo|31edo]]:~~

=== ME scales available in [[31edo]] ===

2 .. 15 16

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30 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2

~~And here are all the~~ ME scales available in [[~~13edo|~~13edo]]:

=== ME scales available in [[13edo]]: ===

2 .. 6 7

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12 . 1 1 1 1 1 1 1 1 1 1 1 2

The ME scales in 31edo will be closer to equal than those in 13edo, since the two step sizes used to approximate equal will differ by a smaller interval (one ~~31th~~ of an octave instead of one 13th).

The ME scales in 31edo will be closer to equal than those in 13edo, since the two step sizes used to approximate equal will differ by a smaller interval (one 31st of an octave instead of one 13th).

The parent edo will better represent smaller edos than larger ones. With edos larger than 1/2 of the parent edo, the step sizes will be 2 and 1, which are, proportionally speaking, far from equal. So 13edo's 3 3 3 4 will sound more like 4edo than its 1 1 1 1 1 1 1 1 1 1 1 2 will sound like 12edo.

@@ Line 9: / Line 9: @@
 (a) and (b) above imply that the ME scale will be a [[MOSScales|moment of symmetry scale]].
-The probably most popular heptatonic ME scale is the major scale of [[12edo|12edo]]: <span style="font-family: monospace; "> 2 2 1 2 2 2 1</span>, but also every [http://en.wikipedia.org/wiki/Diatonic_scale diatonic scale] of 12edo is maximally even. Some more detailed examples follow.
+The probably most popular heptatonic ME scale is the major scale of [[12edo|12edo]]: <span style="font-family: monospace; ">2 2 1 2 2 2 1</span>, but also every [http://en.wikipedia.org/wiki/Diatonic_scale diatonic scale] of 12edo is maximally even. Some more detailed examples follow.
-For instance, here are all the ME scales available in [[31edo|31edo]]:
+=== ME scales available in [[31edo]] ===
 <span style="font-family: Courier,monospace; font-size: 12px; line-height: normal;"> 2 .. 15 16</span>
@@ Line 71: / Line 70: @@
 <span style="font-family: Courier,monospace; font-size: 12px; line-height: normal;"> 30 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2</span>
-And here are all the ME scales available in [[13edo|13edo]]:
+=== ME scales available in [[13edo]]: ===
 <span style="font-family: Courier,monospace; font-size: 12px; line-height: normal;">2 .. 6 7</span>
@@ Line 95: / Line 93: @@
 <span style="font-family: Courier,monospace; font-size: 12px; line-height: normal;"> 12 . 1 1 1 1 1 1 1 1 1 1 1 2 </span>
-The ME scales in 31edo will be closer to equal than those in 13edo, since the two step sizes used to approximate equal will differ by a smaller interval (one 31th of an octave instead of one 13th).
+The ME scales in 31edo will be closer to equal than those in 13edo, since the two step sizes used to approximate equal will differ by a smaller interval (one 31st of an octave instead of one 13th).
 The parent edo will better represent smaller edos than larger ones. With edos larger than 1/2 of the parent edo, the step sizes will be 2 and 1, which are, proportionally speaking, far from equal. So 13edo's 3 3 3 4 will sound more like 4edo than its 1 1 1 1 1 1 1 1 1 1 1 2 will sound like 12edo.